engleski

Some Six-Dimensional Rigid Forms

One can always decompose Dirichlet-Voronoi polytopes of lattices non-trivially into a Minkowski sum of Dirichlet-Voronoi polytopes of rigid lattices. In this report we show how one can enumerate all rigid positive semidefinite quadratic forms (and thereby rigid lattices) of a given dimension d. By this method we found all rigid positive semidefinite quadratic forms for d=5 confirming the list of 7 rigid lattices by Baranovskii and Grishukhin. Furthermore, we found out that for d<=5 the adjacency graph of primitive L-type domains is an infinite tree on which GLd(Z) acts. On the other hand, we demonstrate that in d=6 we face a combinatorial explosion.

dual description, rigid forms, L-type

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